Which of these numbers is prime? ${27,\ 35,\ 40,\ 47,\ 51}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 27 are 1, 3, 9, and 27. The factors of 35 are 1, 5, 7, and 35. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The factors of 47 are 1 and 47. The factors of 51 are 1, 3, 17, and 51. Thus, 47 is a prime number.